Instruction-tuned large language models (LLMs) are capable of generating stories in response to open-ended user requests, but the resulting stories tend to be limited in their diversity. Older, symbolic approaches to story generation (such as planning) can generate substantially more diverse plot outlines, but are limited to producing stories that recombine a fixed set of hand-engineered character action templates. Can we combine the strengths of these approaches while mitigating their weaknesses? We propose to do so by using a higher-level and more abstract symbolic specification of high-level story structure -- implemented via answer set programming (ASP) -- to guide and diversify LLM-based story generation. Via semantic similarity analysis, we demonstrate that our approach produces more diverse stories than an unguided LLM, and via code excerpts, we demonstrate the improved compactness and flexibility of ASP-based outline generation over full-fledged narrative planning.